Q. 54.5( 2 Votes )

Find a point on t

Answer :

Given:


The curve y = x3 – 2x2 – 2x and a line y = 2x – 3


First, we will find The Slope of tangent


y = x3 – 2x2 – 2x


(x3) – (2x2) – (2x)


= 3x3 – 1 (x2 – 1) – 2x1 – 1


= 3x2 – 4x – 2 ...(1)


y = 2x – 3 is the form of equation of a straight line y = mx + c,where m is the The Slope of the line.


so the The Slope of the line is y = 2(x) – 3


Thus, The Slope = 2. ...(2)


From (1) & (2)


3x2 – 4x – 2 = 2


3x2 – 4x = 4


3x2 – 4x – 4 = 0


We will use factorization method to solve the above Quadratic equation.


3x2 – 6x + 2x – 4 = 0


3x(x – 2) + 2(x – 2) = 0


(x – 2)(3x + 2) = 0


(x – 2) = 0 & (3x + 2) = 0


x = 2 or


x =


Substitute x = 2 & x = in y = x3 – 2x2 – 2x


when x = 2


y = (2)3 – 2 (2)2 – 2(2)


y = 8 – (24) – 4


y = 8 – 8 – 4


y = – 4


when x =


y = ()3 – 2 ()2 – 2()


y = () – 2 () + ()


y = () – () + ()


taking lcm


y =


y =


y =


Thus, the points are (2, – 4) & (,)


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